ElectrostaticPotential

class ElectrostaticPotential(configuration, density_mesh_cutoff=None)

A class for calculating the electrostatic potential for a configuration.

Parameters:
absolute()
Returns:

A new grid containing the absolute values (or modulus) of the current field.

Return type:

GridValues

axisProjection(projection_type='sum', axis='c', spin=None, projection_point=None, coordinate_type=<class 'NL.ComputerScienceUtilities.NLFlag._NLFlag.Fractional'>)

Get the values projected on one of the grid axes.

Parameters:

  • projection_type (str) –

    The type of projection to perform. Should be either

    • ’sum’ for the sum over the plane spanned by the two other axes.

    • ’average’ or ‘avg’ for the average value over the plane spanned by the two other axes.

    • ’line’ for the value along a line parallel to the axis and through a point specified by the projection_point parameter.


    Default: ‘sum’

  • axis (str) – The axis to project the data onto. Should be either ‘a’, ‘b’ or ‘c’.
    Default: ‘c’

  • spin (Spin.Sum | Spin.Z | Spin.X | Spin.Y | Spin.Up | Spin.Down | Spin.RealUpDown | Spin.ImagUpDown) – Which spin component to project on.
    Default: Spin.All

  • projection_point (sequence, PhysicalQuantity) – Axis coordinates of the point through which to take a line if projection_type is ‘projection_point’. Must be given as a sequence of three coordinates [a, b, c]. It the numbers have units of length, they are first divided by the length of the respective primitive vectors [A, B, C], and then interpreted as fractional coordinates. Unitless coordinates are immidiately interpreted as fractional.

  • coordinate_type (Fractional | Cartesian) – Flag to toggle if the returned axis values should be given in units of Angstrom (NLFlag.Cartesian) or in units of the norm of the axis primitive vector (NLFlag.Fractional).
    Default: Fractional

Returns:

A 2-tuple of 1D numpy.arrays containing the axis values and the projected data. For Cartesian coordinate type the grid offset is added to the axis values.

Return type:

tuple.

derivatives(x, y, z, spin=None)

Calculate the derivative in the point (x, y, z).

Parameters:

  • x (PhysicalQuantity with type length) – The Cartesian x coordinate.

  • y (PhysicalQuantity with type length) – The Cartesian y coordinate.

  • z (PhysicalQuantity with type length) – The Cartesian z coordinate.

  • spin (Spin.All | Spin.Sum | Spin.Up | Spin.Down | Spin.X | Spin.Y | Spin.Z) – The spin component to project on.
    Default: Spin.All

Returns:

The gradient at the specified point for the given spin. For Spin.All, a tuple with (Spin.Sum, Spin.X, Spin.Y, Spin.Z) components is returned.

Return type:

PhysicalQuantity of type energy × charge-1 × length-1

downsample(downsampling_a=None, downsampling_b=None, downsampling_c=None)

Generate a new GridValues object where the grid is downsampled. Along periodic directions an FFT downsampling is performed. Along non-periodic directions antialiasing and downsampling is performed.

Parameters:

  • downsampling_a (int) – The new number of grid points along the A direction.
    Default: No downsampling.

  • downsampling_b (int) – The new number of grid points along the B direction.
    Default: No downsampling.

  • downsampling_c (int) – The new number of grid points along the C direction.
    Default: No downsampling.

evaluate(x, y, z, spin=None)

Evaluate in the point (x, y, z).

Parameters:

  • x (PhysicalQuantity with type length) – The Cartesian x coordinate.

  • y (PhysicalQuantity with type length) – The Cartesian y coordinate.

  • z (PhysicalQuantity with type length) – The Cartesian z coordinate.

  • spin (Spin.All | Spin.Sum | Spin.Up | Spin.Down | Spin.X | Spin.Y | Spin.Z) – The spin component to project on.
    Default: Spin.All

Returns:

The value at the specified point for the given spin. For Spin.All, a tuple with (Spin.Sum, Spin.X, Spin.Y, Spin.Z) components is returned.

Return type:

PhysicalQuantity of type energy × charge-1

gridCoordinate(i, j, k)

Return the coordinate for a given grid index.

Parameters:

  • i (int) – The grid index in the A direction.

  • j (int) – The grid index in the B direction.

  • k (int) – The grid index in the C direction.

Returns:

The Cartesian coordinate of the given grid index.

Return type:

PhysicalQuantity of type length.

metatext()
Returns:

The metatext of the object or None if no metatext is present.

Return type:

str | None

nlprint(stream=None)

Print a string containing an ASCII table useful for plotting the AnalysisSpin object.

Parameters:

stream (python stream) – The stream the table should be written to.
Default: NLPrintLogger()

primitiveVectors()
Returns:

The primitive vectors of the grid.

Return type:

PhysicalQuantity of type length.

scale(scale)

Scale the field with a float.

Parameters:

scale (float) – The parameter to scale with.

setMetatext(metatext)

Set a given metatext string on the object.

Parameters:

metatext (str | None) – The metatext string that should be set. A value of “None” can be given to remove the current metatext.

shape()
Returns:

The number of grid points in each direction.

Return type:

tuple of three int.

spin()
Returns:

The spin the electrostatic potential is calculated for, always Spin.All.

Return type:

Spin.All

spinProjection(spin=None)

Construct a new GridValues object with the values of this object projected on a given spin component.

Parameters:

spin (Spin.All | Spin.Sum | Spin.X | Spin.Y | Spin.Z) – The spin component to project on.
Default: Spin.All

Returns:

A new GridValues object for the specified spin.

Return type:

GridValues

toArray()
Returns:

The values of the grid as a numpy array slicing off any units.

Return type:

numpy.array

uniqueString()

Return a unique string representing the state of the object.

unit()
Returns:

The unit of the data in the grid.

Return type:

A physical unit.

unitCell()
Returns:

The unit cell of the grid.

Return type:

PhysicalQuantity of type length.

volumeElement()
Returns:

The volume element of the grid represented by three vectors.

Return type:

PhysicalQuantity of type length.

Usage Examples

Calculate the electrostatic potential and save it to a file:

# Set up a configuration.
molecule_configuration = MoleculeConfiguration(
    elements=[Nitrogen, Hydrogen, Hydrogen, Hydrogen],
    cartesian_coordinates=[[ 0.     ,  0.      ,  0.124001],
                           [ 0.     ,  0.941173, -0.289336],
                           [ 0.81508, -0.470587, -0.289336],
                           [-0.81508, -0.470587, -0.289336]]*Angstrom
    )

# Define a calculator.
calculator = LCAOCalculator()
molecule_configuration.setCalculator(calculator)

# Calculate and save the electrostatic potential.
potential = ElectrostaticPotential(molecule_configuration)
nlsave('electrostatic_pot.nc', potential)

nh3_electrostatic_potential.py

For examples on working with 3D grids, see HartreePotential and ElectronDensity.

Notes